A note on confidence intervals

Abstract

If you construct a 95% confidence interval, drawing your data from a population in which the average height is x, then the probability is 0.95 that the confidence interval you construct will include (will “cover”) the true value x. Above are two examples of this fact. In figure 1, the true population average is 6; in figure 2, the population average is 4. In both figures, the interval [5,7] is shown in red. In Figure 1, [5,7] includes the true value 6; in Figure 2, the interval[5,7] does not include the true value 4.